In optical manufacturing and testing, the phrase “absolute testing” is used to describe procedures designed to separate errors in an instrument or reference surface from errors in a part under test (see for example Evans et al, CIRP Annals, 1996). For flats, most commonly used techniques are derived from the well-known 3-Flat test in which three flats are compared pair wise. Where flats are to be used in systems with the optical axis vertical, it is desirable to measure them in that same orientation. Here, however, the three flat test has the problem that the orientation of one flat with respect to gravity must be changed and, hence, the gravitational deformation changes.
The invention described herein allows high accuracy testing of flats, using just two flats, in any orientation. Because only two flats are required, no change in orientation relative to gravity is required and hence no change in mount induced deformation occurs.
There is substantial literature on the so-called “absolute testing” of optical flats (see, for example, Evans Chris J. and Kestner Robert N. “Test Optics Error Removal” Applied Optics, 1996, Vol 35, No 7, 1015-21). One general approach is to measure multiple objects in different combinations and then to determine the contributions from each object individually such as in the well-known 3-Flat test. The 3-Flat test has a variety of limitations. One of the most significant is the need for three, nominally identical parts to test. Another is that the test generates only two profiles on the part, not information on the entire surface. A third limitation is that the interchanging of flats necessarily inverts the effect of gravity on one of the flats if measurements are made with the optical axes of the flats vertical, a common requirement.
These limitations may be alleviated by the use of lateral shearing (mechanical shift) in two orthogonal directions, proposed by a number of authors—most recently Elster, Clemens, “Exact two-dimensional wave-front reconstruction from lateral shearing interferograms with large shears,” Appl Opt, V39, No 29, 10 Oct. 2000, pp 5353-5359. The method is, however, sensitive to drift (.e.g mechanical drift of the part relative to the instrument) and noise.
A number of authors (e.g., Fritz, Bernard S. “Absolute Calibration of an Optical Flat” Optical Engineering, 1984, Vol 23, No 4, 379-83, Evans Chris J. and Kestner Robert N. “Test Optics Error Removal” Applied Optics, 1996, Vol 35, No 7, 1015-21) have described rotational shears, which are robust, but only sensitive to components of the surfaces under test which are rotationally varying (RV) (i.e., vary with azimuthal angle θ in a polar coordinate system) using averaging, Fourier analysis, or other algorithms. Such methods can be combined with a 3-Flat test to generate a full surface map with both RV and rotationally invariant (RI) terms (e.g., Fritz (1984) supra, Evans and Kestner (1996) supra, Bourgeois, Robert P., Joann Magner, and H. Philip Stahl, “Results of the Calibration of Interferometer Transmission Flats for the LIGO Pathfinder Optics”, SPIE Vol. 3134, pp 86-94 (1997), and Freishlad, (U.S. Pat. No. 6,184,994)). Such techniques do not, however, solve the problem of measurement of flats where the optical axis is vertical.
Another class of procedures combine a rotational shear and a lateral shear. Ichikawa and Yamamoto (e.g., U.S. Pat. No. 5,982,490) describe apparatus and procedures for absolute calibration using averaging of rotationally sheared data to obtain the RV terms and a lateral shear to obtain the RI term. Dörband, Bernd and Günther Seitz, “Interferometric testing of optical surfaces at its current limit”, Optik 112, No. 9 (2001), pp 392-398 describe the application of similar procedures. It is well known that a change in the tilt of the part that is moved during the mechanical translation (shear) causes an error in the quadratic term (in a polynomial expansion, such as Zernike polynomials, which is often referred to as power in the optical community; this error is of little concern in the testing of spherical optics (where the radius of curvature is usually toleranced separately). For flats, however, this is a serious concern.
Note that the change in tilt of the part being moved (tilt error) includes both the angular error motion of the translation mechanism and any drift (e.g. thermally induced) in the mounting of the part that is moved to the translation mechanism.
Evans (1996) supra briefly described an experiment in which the tilt error during translation was measured using an autocollimator and then corrected (limited by the resolution of the autocollimator) before the second (sheared) data set was taken. These experiments were performed with a horizontal optical axis, and the agreement with other methods poor in the quadratic term.
Consequently, it is a primary object of the present invention to provide apparatus and methods by which optical flats may be absolutely measured while compensating for the effects of differences in orientation.
Other objects of the invention will be obvious and appear hereinafter when the following detailed description is read in connection with the appended drawings.